Details for entry \(A_4(8,3)\)

Lower bounds

• echelon_ferrers ( show
  optimal [(), (0, 1, 2, 3), (0, 1, 2, 4, 7), (0, 1, 3, 5, 7), (0, 1, 4, 5), (0, 1, 6), (0, 2, 3, 4, 5), (0, 2, 3, 6, 7), (0, 2, 4, 6), (0, 2, 5, 7), (0, 3, 4, 7), (0, 3, 5, 6), (1, 2, 3, 4, 5, 6), (1, 2, 5), (1, 2, 6, 7), (1, 3, 4), (3, 4, 5, 6, 7)] (if conjecture about Ferrers Diagram Rank-Metric Codes is true: 16881731 with optimal [(), (0, 1, 2, 3), (0, 1, 2, 4, 7), (0, 1, 3, 5, 7), (0, 1, 4, 5), (0, 1, 6), (0, 2, 3, 4, 5), (0, 2, 3, 6, 7), (0, 2, 4, 6), (0, 2, 5, 7), (0, 3, 4, 7), (0, 3, 5, 6), (1, 2, 3, 4, 5, 6), (1, 2, 5), (1, 2, 6, 7), (1, 3, 4), (3, 4, 5, 6, 7)])
  ) : 16881731
• ef_computation ( show
  [(0, 1, 2, 3), (0, 1, 4, 5), (0, 1, 2, 4, 7), (1, 2, 5), (0, 2, 3, 4, 5), (0, 1, 6), (0, 2, 4, 6), (1, 3, 4), (0, 1, 3, 5, 7), (0, 2, 3, 6, 7), (0, 3, 5, 6), (0, 3, 4, 7), (0, 2, 5, 7), (1, 2, 6, 7), (3, 4, 5, 6, 7), (), (1, 2, 3, 4, 5, 7)]
  ) : 16881731
• improved_cdc_lower_bound ( ) : 16874323
• layer_construction ( ) : 16874323
• cdc_lower_bound ( ) : 16874321
• cdc_average_argument ( ) : 5258186
• gilbert_varshamov ( ) : 293502
• trivial_4 ( ) : 2
• trivial_2 ( ) : 0

Upper bounds

• johnson_MDC_Proposition_5 ( ) : 20449159
• heinlein_ihringer_semidefinite_programming ( ) : 20482322
• special_improved_cdc_upper_bound ( ) : 20519573
• improved_cdc_upper_bound ( ) : 20519575
• cdc_upper_bound ( ) : 20519577
• relax_d ( ) : 6269331761
• trivial_3 ( ) : 9371059621

Do you have better bounds?